Use of undoped crystals of the yttrium/aluminum/borate family for creating non-linear effects

ABSTRACT

The present invention concerns a method of producing blue or UV light. To produce blue or UV light with the described crystal family it is proposed according to the invention that a crystal of the family A x M 1-x X 3 (BO 3 ) 4 , wherein both A and also M stand for an element from the group Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, A≠M and X═Al, Ga, Sc and 0≦x≦1, is used as a non-linear optical element to produce light of a wavelength of less than 0.450 μm.

The present invention concerns a method of producing coherent blue or ultraviolet light, the use of crystals of the yttrium/aluminum/borate family for producing coherent blue or ultraviolet light and crystals of the yttrium/aluminum/borate family which are especially adapted for producing coherent blue or ultraviolet light.

Scientific and Technical Fundamentals

Solid-state lasers which produce laser light in the blue or UV range are important light sources for numerous applications in technical regions involving a high market potential such as for example micromachining, precision measurement engineering, semiconductor production, biotechnology, medical engineering, display and printing technologies and so forth.

The desired wavelengths for such applications are in the spectral range of shorter than 450 nm. UV wavelengths which can be produced by non-linear frequency conversion from common (so-called fundamental) wavelengths assume a particular place. Thus for example the wavelengths which can be produced by the Nd³⁺ junctions in widely varying laser host crystals in the range of 1.047-1.080 μm: 0.349-0.360 μm (frequency tripling), 0.261-0.270 μm (quadrupling), 0.209-0.216 μm (quintupling). Further examples are based on fundamental wavelengths of Yb³⁺ in the range of 0.980-1.100 μm (accordingly the ranges 0.326-0.366, 0.24 -0.275 and 0.196-0.220 μm can be covered in a similar manner), Pr³⁺ in the range of 0.490-0.730 μm (for the range of 0.245-0.365 μm by frequency doubling), and so forth. Fundamental wavelengths can be produced by numerous laser sources (for example diode-pumped solid-state lasers, diode lasers, fiber lasers) in the range which is of interest for the various frequency conversion options. Crystals with corresponding non-linear optical (NLO) properties then permit the desired frequency conversion. NLO crystals for a given application must fulfill the following general requirements:

phase-adaptable for the desired frequency conversion,

transparent for the fundamental and converted wavelengths, conversion. NLO crystals for a given application must fulfill the following general requirements:

phase-adaptable for the desired frequency conversion,

transparent for the fundamental and converted wavelengths,

low optical losses and high destruction threshold for operation as a light source,

favorable properties for crystal growth and machining so that commercially useable NLO components can be produced, and

sufficiently great effective non-linearity.

Known commercially useable NLO crystals which are suitable for frequency conversion into the blue or ultraviolet frequency spectrum are BBO (BaB₂O₄, β-barium borate), LBO (LiB₃O₅, lithium triborate), YCOB (YCa₄O(BO₃)₃, BiBO (BiB₃O₆, bismuth borate) and CLBO (CsLiB₆O₁₀).

BBO, LBO, YCOB and BiBO permit frequency tripling of the wavelength 1.064 μm. Those NLO crystals, by so-called sum frequency generation of two wavelengths (in the case described here 1.064μm=λ and its second harmonic 0.532 μm=λ/2) permit the production of the third harmonic at 0.355 μm=λ/3. In the so-called type I the mixed wavelengths involve the same polarization while in the so-called type II they are orthogonally polarized.

Even if basically non-linear effects occur in the crystal their efficiency depends on further secondary conditions. Thus for high-efficiency SFG it is necessary for both the irradiated wave or waves and also the wave or waves produced in the crystal to constructively interfere. To achieve that phase adaptation must be effected, that is to say it is necessary to look for a propagation direction in the crystal, in respect of which both the energy and the pulse are obtained in frequency conversion. That is achieved if the propagation speeds of the waves in that direction are the same. The phase adaptation angles or orientation angles are defined in FIG. 1:

A detailed summary of NLO crystal data is to be found in the reference Nik 03. Supplemental information is to be found in Eim 87, Ger 03 and Pel 06. Those references also describe the chemical compositions and the substantial material properties.

BBO and CLBO can be used commercially as NLO crystals for frequency doubling (or SHG for second harmonic generation) of 0.532 μm. Frequency quadrupling of 1.064 μm is also to be understood as frequency doubling of 0.532 μm=λ to produce UV light at 0.266 μm=λ/2.

The commercially available NLO crystals which can be considered for the production of blue or UV laser sources have the following limitations in their areas of application:

BBO: the disadvantages of BBO are the moisture sensitivity of the material (therefore the surfaces are unstable and relatively difficult to polish and coat) and the disadvantageous angle acceptance and the “walk-off”. The latter limit the focusability of the fundamental waves and the useable crystal lengths.

LBO: the disadvantages of LBO are the moisture sensitivity of the material and the lack of phase adaptability for short wavelengths (below 555 nm SHG is no longer possible).

YCOB: the disadvantages of YCOB and other members of this crystal family are the low non-linear coefficients and the lack of phase adaptability for short wavelengths (below 720 nm SHG is not possible).

CLBO: this crystal, due to extremely severe moisture sensitivity, raises problems which are difficult to insoluble in terms of crystal polishing. Therefore CLBO is used only in few cases.

BiBO: this material cannot be used for wavelengths below 290 nm because the transparency range of this material is limited. The destruction threshold at 355 nm is markedly too low for the desired areas of use. BIBO can only be used for special UV applications in a limited range. Important wavelengths such as for example 266 nm cannot be produced with BiBO.

Nd_(x)Y_(1-x)Al₃(BO₃)₄ (abbreviated as NYAB), Yb_(x)Y_(1-x)Al₃(BO₃)₄ (YbYAB) and Nd_(x)Gd_(1-x)Ga₃(BO₃)₄ (NGAB) are known crystals of which it is known that they exhibit non-linear optical properties.

NYAB or NGAB which have self-doubling properties are in principle of less interest as the laser-active ions have additional unwanted optical absorption bands in the transmission range. Nonetheless they are of interest in some situations of use.

As an example here, the properties of YAB are described in greater detail and the state of the art analyzed.

Properties of yttrium aluminum borate (YAB) YAB crystals have the following features:

Structure and material parameters structure trigonal, space group R32 lattice constant a = 9.287 Å c = 7.256 Å density 3.70 g/cm³ melting point non-congruent hardness Mohs 7.5 stability non-hygroscopic specific heat 0.75 W s g⁻¹K⁻¹ thermal conductivity 3-4 W m⁻¹K⁻¹ Optical parameters transmission 160-2200 nm refractive indices n_(o) = 1.7553 (at 1064 nm) n_(e) = 1.6869 (at 1064 nm) uniaxially negative (n_(o) > n_(e))

The relatively great hardness of YAB crystals and their insensitivity in relation to air moisture must be emphasized here. Those two properties distinguish YAB crystals from many other borates such as BBO, LBO and CLBO. The latter crystals (see above) at the present time form the standards among the NLO materials for UV applications. YAB crystals afford marked advantages due to hardness and stability. Surface polishing of YAB crystals can be effected with conventional polishing procedures (using water). The surfaces can be cleaned with aqueous solvents. The application of surface treatments for controlling surface reflectivity by means of thin layer technology is similar in relation to YAB as to optical glasses (for example quartz glass) or oxidic crystals (for example Y₃A₅O₁₂), that is to say very much simpler than in the case of hygroscopic materials such as BBO, LBO and CLBO.

The NLO properties which can be extrapolated for YAB from the literature are summarized in Table 1 for SHG and in Table 2 for SFG. With one exception that information involves data which were measured with self-doubling crystals of the type NYAB (═Nd_(x)Y_(1-x)Al₃(BO₃)₄ with x=between 4 and 20%), NGAB (═Nd_(x)Gd_(1-x)Al₃(BO₃)₄ with x=between 3 and 10%) or YbYAB (═Yb_(x)Y_(1-x)Al₃(BO₃)₄ with x=between 5 and 10%). The exception is the reference Unt 91 which actually refers to an undoped “pure” YAB crystal. That reference is analyzed in detail hereinafter.

The listed data provide the following insights:

the values measured with NYAB, NGA or YbYAB for the ordinary and extraordinary refractive indices n_(o) and n_(e) originate from various works (Dor 81, Lu 89, Luo 89, Tu 00): the dispersion of the refractive indices is precisely known over a limited range of about: between 0.404 and 0.707 μm, beyond that extrapolation is required. Such extrapolation leads to severe deviations in the case of short UV and in the case of IR wavelengths.

The phase adaptation angles vary between 28.5 and 34.5° for SHG (1.064 mm) type I and between 41.0 and 51° for SHG type II. The scatter of those angle values is probably in part because of the differences in the refractive indices which formed the basis for calculation of the phase adaptation conditions.

the shortest wavelength produced with SHG and demonstrated is at 0.455 μm.

many experimental parameters (for example the NLO coefficients d_(eff) or the angle acceptances) are known only in part and in fragmentary fashion. The angle dependency of d_(eff) is not taken into consideration although ultimately it determines the efficiency of the NLO process.

TABLE 1 Type I Type II Type Angle Angle SHG Type Type I II acceptance acceptance λ λ/2 Type I II d_(eff) d_(eff) mrad mrad μm n_(o) n_(e) μm n_(o) n_(e) Angle ° Angle ° pm/V pm/V cm cm Ref. 0.910 0.455 34.0 Bar97 1.064 1.762 1.693 0.532 1.7780 1.7037 30 Dor81 1.064 1.765 1.694 0.532 1.786 1.710 30 43 0.66 1.01 Dor83 1.064 1.7553 1.6863 0.532 1.7808 1.7050 34.53 50.57 Lu89 1.064 1.7553 1.6869 0.532 1.7808 1.7075 32.9 51 1.43 0.67 Luo89 1.062 1.7617 1.6904 0.531 1.7795 1.7045 28.46 41.03 Luo89b 1.064 1.7553 1.6869 0.532 1.7808 1.7075 32.9 1.30 Sch90 1.06  0.53 33 Unt91 1.06  1.7613 1.6886 0.53 1.7819 1.7064 30.7 45.6 1.273 0.725 Fan92 1.064 0.532 32.9 0.67 Hwa93 1.062 0.531 30.7 Bar97b 1.062 0.531 30.7 Jaq98 1.016-1.090 0.508-0.545 31 1.2-1.45 Dek03 Dek04 1.318 1.762 1.693 0.659 1.778 1.704 27 36 0.99 1.52 Dor83 1.338 0.669 1.2 Jaq99 0.710 0.355 43.75 Bre04a 1.064 1.760 1.688 0.532 1.780 1.705 30.08 44.36 Tu00 1.062 0.531 30.08 Bre01 1.338 0.669 27.8 Bre04b

TABLE 2 Type I Type II Type Angle Angle SFG Type Type I II acceptance acceptance λ 1 λ 2 λ 3 Type I II d_(eff) d_(eff) mrad mrad μm μm μm Angle ° Angle ° pm/V pm/V cm cm Ref. 1.064 0.532 0.355 41 62 0.33 0.51 Dor83 1.062 0.807 0.459 35 Jaq98 1.338 0.750 0.480 30.8 Jaq99 1.062 0.588 0.379 38.2 Bre02 1.062 0.748 0.439 35 Bre01 1.317 1.062 0.588 27.3 Bre02

Based on the values derived from the literature items in Tables 1 and 2 that gives a picture of the NLO properties of YAB and RE_(x)Y_(1-x)Al₃(BO₃)₄ crystals, which has many gaps.

Before answering the question as to whether those crystals represent a possible supplement to BBO, LBO and CLBO for applications in the blue and UV range and which NLO parameters have to be taken into account in the production of YAB and RE_(x)Y_(1-x)Al₃(BO₃)₄ crystals to obtain commercially useable NLO components, the relevant patent literature will firstly also be evaluated in respect of YAB and RE_(x)Y_(1-x)Al₃(BO₃)₄.

Patent literature

U.S. Pat. No. 5,030,851 “RE_(x)Y_(1-x)Al₃(BO₃)₄ crystals in electro-optic and nonlinear devices”

US patent application US 2006/0054864 A1 “Method and Structure for Nonlinear Optics”

-   U.S. Pat. No. 5,030,851 (1991)

This document proposes using NYAB in such a way that laser effect and production of the harmonic wavelengths occur in separate crystals: NYAB is used as a normal, stand-alone NLO crystal and the Nd ions are no longer required as they lead to unwanted absorption effects. It is therefore proposed that YAB crystals be used for frequency doubling. That document does not include any more precise information about phase adaptability of NYAB and YAB for shorter wavelengths (than 1.06 μm). There is also no reference to the angle dependency of the NLO coefficients.

The uses of YAB and crystals from the A_(x)M_(1-x)X₃(BO₃)₄ family for the production of UV radiation is also not mentioned.

-   US 2006/0054864 A1

That document describes the crystal growth of A_(x)M_(1-x)Al₃B₄O₁₂ by means of high temperature solvents which permit greatly reduced contamination with effects which are disadvantageous in regard to transmission in the UV wavelength range.

The available scientific and patent literature permits the following conclusions to be drawn:

the NLO properties of the self-doublers NYAB, NGAB and YbYAB are investigated in a restricted scope. The measured and calculated parameters involve numerous inconsistencies starting with the important parameter of phase adaptation angle.

the NLO properties of undoped crystals such as YAB, GAB, LuAB and RE_(x)Y_(1-x)Al₃(BO₃)₄ are substantially unknown in the literature. U.S. Pat. No. 5,030,851 only mentions wavelengths outside the blue or ultraviolet range:

the advantages of RE_(x)Y_(1-x)Al₃(BO₃)₄ crystals which, by virtue of their mechanical and chemical properties, can be sawn, ground, polished, cleaned and coated with conventional material treatment procedures have hitherto not been investigated.

DESCRIPTION OF THE INVENTION

Taking the described state of the art as the basic starting point therefore the object of the invention is to provide a novel method of producing blue or ultraviolet laser light. A further object of the invention is to provide a crystal with which blue or ultraviolet laser light can be produced and which has low moisture sensitivity, high transparency and a very high destruction threshold as well as favorable mechanical and chemical properties and is therefore suitable for industrial manufacture.

That object is attained in that a crystal of the family A_(x)M_(1-x)X₃(BO₃)₄ is used as a non-linear optical element to produce light of a wavelength of less than 0.450 μm. In that case both A and also M stand for an element from the group Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, wherein however A≠M and X═Al, Ga, Sc and 0≦x≦1.

The stated crystal family A_(x)M_(1-x)X₃(BO₃)₄ also includes as members thereof known crystals such as Nd_(x)Y_(1-x)Al₃(BO₃)₄ (abbreviated as NYAB), Yb_(x)Y_(1-x)Al₃(BO₃)₄ (YbYAB) and Nd_(x)Gd_(1-x)Ga₃(BO₃)₄ (NGAB).

In a preferred embodiment our invention permits the use of various A_(x)M_(1-x)X₃(BO₃)₄ crystals as independent NLO crystals for frequency conversion by frequency doubling (SHG for second harmonic generation), frequency tripling (THG for third harmonic generation), sum frequency generation (SFG), and so forth. The use of the crystals YAl₃(BO₃)₄ (abbreviated as YAB), GdAl₃(BO₃)₄ (abbreviated as GAB) and LuAl₃(BO₃)₄ (abbreviated as LuAB) is particularly preferred. Mixed crystals such as for example Y_(x)Lu_(1-x)Al₃(BO₃)₄ (abbreviated as LuYAB) can also be of interest.

The object of the present invention is to provide a method of producing important components for various lasers with short wavelengths (below 450 nm), which has substantial technical and economic advantages over the known NLO methods. That object is based on the NLO properties of A_(x)M_(1-x)X₃(BO₃)₄ with A=Y, La, rare earths, M=Y, La, rare earths, X═Al, Ga, Sc, 0≦x≦1 or x=0 or x=1) crystals. That permits the production of laser beams of wavelengths 360, 355, 349, 270, 266, 262 nm (by tripling and quadrupling the frequency of the fundamental wave of for example an Nd laser), between 326 and 353, between 250 and 265 nm (by tripling and quadrupling of the frequency of for example a Yb laser), 360.5 +/−2, 320+/−2, 303.5+/−2, 261.5+/−2 nm (by frequency doubling of for example a Pr laser), with frequency doubler crystals which unlike previously used materials (for example BBO or CLBO) have favorable mechanical and chemical properties and are therefore suitable for an industrial manufacture. The list of the possible wavelengths which can be achieved is not limited to the aforementioned selection and can be expanded without any problem to further fundamental wavelengths of for example semiconductor laser diodes or fiber lasers. The properties of these novel frequency conversion materials are now described by reference to some examples.

The NLO crystals A_(x)M_(1-x)X₃(BO₃)₄ (with A=Y, La, rare earths, M=Y, La, rare earths and X═Al, Ga, Sc, 0≦x≦1 or x=0 or x=1) are materials with extraordinary properties for NLO applications in the UV wavelength range and with mechanical and chemical properties which are extraordinary for UV NLO materials (hardness, stability, insensitivity to moisture). Accordingly A_(x)M_(1-x)X₃(BO₃)₄ crystals can be processed inexpensively and with conventional optical polishing procedures.

A_(x)M_(1-x)X₃(BO₃)₄ belong to the space group R32 and have a trigonal unit cell with lattice constants a=0.925-0.979 and c=0.718-0.795 nm depending on the respective composition. The axes of the optical ellipsoid are so defined that X=a and Z=c (Y is thus afforded automatically). The orientation that the propagation direction has in an NLO sample is described in the XYZ system by means of two polar angles Phi (in the XY plane, starting from X) and Theta (in the plane of Z and projection of the direction onto the XY plane, starting from Z).

It has been found that A_(x)M_(1-x)X₃(BO₃)₄ crystals afford numerous phase adaptation possibilities which can be used for the production of UV light. All the above-mentioned and other wavelengths between 0.250 and 0.360 μm can be produced. The NLO coefficients for that wavelength are in the range>0.30 μm/V. Contrary to assertions in the literature however those crystals cannot be efficiently phase-adapted over the entire transmission range. The shortest phase-adaptable wavelength theoretically occurs at about 0.491 μm (which would correspond to frequency-doubled UV light at 0.245 μm), but the corresponding d_(eff) coefficient is greater than 0.30 μm/V only at wavelengths above 0.498 μm.

To produce blue or ultraviolet light with the described crystal family it is necessary to suitably adapt the crystal.

The simplest possible way of passing an electromagnetic wave through the crystal is to direct the electromagnetic wave in the normal direction, that is to say perpendicularly onto a crystal end face (normal incidence). For that purpose according to the invention the crystal has at least two substantially flat end faces, wherein one of the end faces is oriented relative to the crystallographic axes in such a way that with normal incidence of an electromagnetic wave or two electromagnetic waves of different wavelengths onto that end face, by virtue of a non-linear optical effect, an electromagnetic wave of a wavelength of less than 0.450 μm is produced. Particularly preferably the crystal end face is perpendicular to the preferred propagation direction defined in Tables 3 through 5.

Alternatively thereto the crystal has at least one end face which is oriented relative to the crystallographic axes in such a way that, upon the incidence of an electromagnetic wave or two electromagnetic waves of different wavelengths onto that end face, at the Brewster angle, by virtue of a non-linear optical effect, an electromagnetic wave of a wavelength of less 0.450 μm is produced.

More specifically if light is directed onto the crystal end face at the Brewster angle the light components with a polarization parallel to the plane of incidence are not reflected but transmitted without losses worth mentioning.

The particularly preferred embodiments are disclosed in the following examples in the cases SHG type I, SHG type II, THG and SFG type I, THG and SFG type II, and the corresponding parameters are so represented that NLO components can be readily produced, with crystals A_(x)M_(1-x)X₃(BO₃)₄.

Examples Example A

SHG with YAB

A particularly preferred possible way of producing blue or ultraviolet light involves the use of a YAB crystal. An electromagnetic wave of the wavelength λ is passed through the crystal. In that case the crystal is used to produce the second harmonic (0.5λ), that is to say to produce an electromagnetic wave of half the wavelength.

In that case an electromagnetic wave of the wavelength λ is advantageously passed through the crystal in such a way that the propagation direction includes an angle θ with the optical Z-axis and an angle φ with the optical X-axis so that the crystal is used to produce the second harmonic of the wavelength 0.5λ.

Table 3 summarizes preferred values for the parameters λ, θ, φ and 0.5λ. The parameters respectively assume the values of a line in the Table, in preferred embodiments.

TABLE 3 SHG Type Type λ λ/2 Type I II Type I II μm μm θ ° θ ° φ° φ° 0.492 0.246 85.4 0 0.502 0.251 77.1 0 0.532 0.266 66.2 0 0.622 0.311 51.1 0 0.742 0.371 41.2 65.6 0 30 0.802 0.401 38.1 58.3 0 30 0.912 0.456 34.0 50.3 0 30 0.942 0.471 33.2 48.8 0 30

In that respect a distinction is drawn between type I and type II.

In the case of type I for example an electromagnetic wave of the wavelength 0.742 μm is passed through the crystal in such a way that the propagation direction includes an angle of 41.2° with the optical Z-axis and an angle of 0° with the optical X-axis so that the crystal is used to produce the second harmonic of the wavelength 0.371 μm.

In the case of type II for example an electromagnetic wave of the wavelength 0.742 μm is passed through the crystal in such a way that the propagation direction includes an angle of 65.6° with the optical Z-axis and an angle of 30° with the optical X-axis so that the crystal is used to produce the second harmonic of the wavelength 0.371 μm.

Example B

THG with YAB

A further particularly preferred possible way of producing blue or ultraviolet light also involves the use of a YAB crystal. An electromagnetic wave of the wavelength λ is passed through the crystal. In that case the crystal is used to produce the third harmonic (⅓λ), that is to say to produce an electromagnetic wave of a wavelength which is shorter by the factor of ⅓ (frequency tripling).

In that case an electromagnetic wave of the wavelength λ is advantageously passed through the crystal in such a way that the propagation direction includes an angle θ with the optical Z-axis and an angle φ with the optical X-axis so that the crystal Is used to produce the second harmonic of the wavelength ⅓λ.

Table 4 summarizes preferred values for the parameters λ, θ, φ and ⅓λ. In preferred embodiments the parameters respectively assume the values of a line in the Table. As in this case an electromagnetic wave of double the frequency or half of the wavelength is also produced, which however is at least partially absorbed by the crystal again to produce the electromagnetic wave of the wavelength ⅓λ, the wavelength λ/2 is also specified for the sake of completeness.

TABLE 4 THG Type Type λ 1 λ/2 λ/3 Type I II Type I II μm μm μm θ ° θ ° φ° φ° 0.710 0.355 0.237 79.8 0 0.810 0.405 0.270 58.4 0 0.950 0.475 0.317 46.5 60.3 0 30 1.030 0.515 0.343 42.3 53.6 0 30 1.060 0.530 0.353 41.0 51.6 0 30 1.340 0.670 0.447 33.2 40.7 0 30

In this case also a distinction is drawn between type I and type II, as in Example A.

Example C

SFG with YAB

Still a further particularly preferred possible way of producing blue or ultraviolet light also involves the use of a YAB crystal. Here a first electromagnetic wave of the wavelength λ₁ and a second electromagnetic wave of the wavelength λ₂ is passed through the crystal in such a way that the propagation direction includes an angle θ with the optical Z-axis and an angle φ with the optical X-axis, and the crystal is used to produce an electromagnetic wave of the wavelength λ₃=λ₁·λ₂/(λ₁+λ₂). The crystal is therefore used to produce an electromagnetic wave at a frequency corresponding to the sum of the frequencies of the irradiated waves.

Alternatively thereto a first electromagnetic wave of the wavelength λ₃ and a second electromagnetic wave of the wavelength λ₂ can also be passed through the crystal in such a way that the propagation direction includes an angle θ+/−Δθ with the optical Z-axis and an angle φ+/−Δφ with the optical X-axis, and the crystal is used to produce an electromagnetic wave of the wavelength λ₁=λ₂·λ₃/(λ₂−λ₃). The crystal is therefore used to produce an electromagnetic wave of a frequency corresponding to the difference in the frequencies of the irradiated waves.

Finally it is also possible to pass an electromagnetic wave at the frequency λ₃ through the crystal in such a way that the propagation direction includes an angle θ+/−Δθ with the optical Z-axis and an angle φ+/−Δθ with the optical X-axis and the crystal is used to produce an electromagnetic wave of the wavelength λ₁ and an electromagnetic wave of the wavelength λ₂. The crystal is therefore used for a parametric process which involves producing from an irradiated electromagnetic wave two electromagnetic waves of another frequency, the frequency of the irradiated wave being the sum of the frequencies of the waves produced.

Table 5 summarizes preferred values for the parameters λ₁, λ₂, λ₃, θ, φ. In preferred embodiments the parameters assume the values of a respective line in the Table.

Type I λ₁ λ₂ λ₃ Theta (μm) +/− (μm) +/− (μm) +/− (°) +/− 0.015 0.015 0.010 3.0° Δθ (°) φ (°) Δφ (°) 1.344 0.881 0.532 30.5 3.0 0 5 1.554 0.809 0.532 30.2 3.0 0 5 0.810 0.632 0.355 42.9 3.0 0 5 1.064 0.532 0.355 40.8 3.0 0 5 0.642 0.454 0.266 64.5 3.0 0 5 0.722 0.421 0.266 62.2 3.0 0 5 0.812 0.396 0.266 59.6 3.0 0 5 0.982 0.365 0.266 55.1 3.0 0 5 1.062 0.355 0.266 53.3 3.0 0 5 1.342 0.332 0.266 48.0 3.0 0 5 1.064 0.266 0.213 72.1 3.0 0 5 1.326 0.254 0.213 61.5 3.0 0 5 0.720 0.355 0.238 77.8 3.0 0 5 0.720 0.520 0.302 52.4 3.0 0 5 0.910 0.720 0.402 37.7 3.0 0 5 0.910 0.808 0.428 35.8 3.0 0 5 1.064 0.532 0.355 40.8 3.0 0 5 1.062 0.589 0.379 38.7 3.0 0 5 1.062 0.751 0.440 34.6 3.0 0 5 1.062 0.808 0.459 33.6 3.0 0 5 1.338 0.749 0.480 32.0 3.0 0 5 1.338 0.806 0.503 31.2 3.0 0 5 1.344 0.881 0.532 39.2 2.5 30 5 1.554 0.809 0.532 36.8 2.5 30 5 0.810 0.632 0.355 62.6 2.5 30 5 1.064 0.532 0.355 51.5 2.5 30 5 0.982 0.365 0.266 70.0 2.5 30 5 1.062 0.355 0.266 64.9 2.5 30 5 1.342 0.332 0.266 54.4 2.5 30 5 1.326 0.254 0.213 69.9 2.5 30 5 0.910 0.720 0.402 53.0 2.5 30 5 0.910 0.808 0.428 51.5 2.5 30 5 1.064 0.532 0.355 51.4 2.5 30 5 1.062 0.589 0.379 49.5 2.5 30 5 1.062 0.751 0.440 46.2 2.5 30 5 1.062 0.806 0.459 45.6 2.5 30 5 1.338 0.749 0.480 39.9 2.5 30 5 1.338 0.806 0.503 39.5 2.5 30 5 1.344 0.881 0.532 51.7 2.5 30 5 1.554 0.809 0.532 57.0 2.5 30 5 0.910 0.720 0.402 64.2 2.5 30 5 0.910 0.808 0.428 56.3 2.5 30 5 1.062 0.751 0.440 59.5 2.5 30 5 1.062 0.808 0.459 55.2 2.5 30 5 1.338 0.749 0.480 59.7 2.5 30 5 1.338 0.806 0.503 55.6 2.5 30 5

REFERENCES

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1. A method of producing blue or ultraviolet light characterized in that a crystal of the family A_(x)M_(1-x)X₃(BO₃)₄, wherein both A and also M stand for an element from the group Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, A≠M and X═Al, Ga, Sc and 0≦x≦1, is used as a non-linear optical element to produce light of a wavelength of less than 0.450 μm.
 2. A method as set forth in claim 1 characterized in that YAl₃(BO₃)₄, GdA₃(BO₃)₄, YbAl₃(BO₃)₄ or LuAl₃(BO₃)₄ is used as the crystal
 3. A method as set forth in claim 1 or claim 2 characterized in that an electromagnetic wave of the wavelength λ is passed through the crystal and the crystal is used to produce the second harmonic (0.5λ) which is of a wavelength of less than 0.450 μm.
 4. A method as set forth in claim 3 characterized in that an electromagnetic wave of the wavelength λ is passed through the crystal in such a way that the propagation direction includes the angle θ+/−Δθ with the optical axis Z and the angle φ+/−Δφwith the optical axis X and the crystal is used to produce the second harmonic of the wavelength 0.5λ, wherein λ, θ, Δθ, φ, Δφ and 0.5λ assume the values of a line in the following Table: λ 0.5 λ (μm) +/− (μm) 0.001 θ (°) Δθ (°) φ (°) Δφ (°) 0.498 +/− 0.002 0.249 79.58 2.50 0 1.5 0.502 +/− 0.002 0.251 77.13 2.00 0 1.5 0.506 +/− 0.002 0.253 75.10 2.00 0 1.5 0.510 +/− 0.002 0.255 73.35 2.00 0 1.5 0.514 +/− 0.002 0.257 71.79 1.50 0 1.5 0.519 +/− 0.002 0.2595 70.04 1.50 0 1.5 0.523 +/− 0.002 0.2615 68.77 1.50 0 1.5 0.527 +/− 0.002 0.2635 67.60 1.50 0 1.5 0.531 +/− 0.002 0.2655 66.49 1.50 0 1.5 0.535 +/− 0.002 0.2675 65.46 1.00 0 1.5 0.540 +/− 0.002 0.270 64.24 1.00 0 1.5 0.545 +/− 0.002 0.2725 63.11 1.00 0 1.5 0.550 +/− 0.002 0.275 62.04 1.00 0 1.5 0.560 +/− 0.002 0.280 60.07 1.00 0 1.5 0.570 +/− 0.002 0.285 58.30 1.00 0 1.5 0.580 +/− 0.002 0.290 56.68 1.00 0 1.5 0.590 +/− 0.002 0.295 55.19 1.00 0 1.5 0.600 +/− 0.002 0.300 53.81 1.00 0 1.5 0.604 +/− 0.002 0.302 53.29 1.00 0 1.5 0.608 +/− 0.002 0.304 52.78 1.00 0 1.5 0.612 +/− 0.002 0.306 52.29 0.75 0 1.5 0.636 +/− 0.002 0.318 49.59 0.75 0 1.5 0.640 +/− 0.002 0.320 49.18 0.75 0 1.5 0.644 +/− 0.002 0.322 48.78 0.75 0 1.5 0.709 +/− 0.002 0.3545 43.36 0.75 0 1.5 0.713 +/− 0.002 0.3565 43.08 0.75 0 1.5 0.717 +/− 0.002 0.3585 42.81 0.75 0 1.5 0.721 +/− 0.002 0.3605 42.54 0.75 0 1.5 0.725 +/− 0.002 0.3625 42.28 0.75 0 1.5 0.729 +/− 0.002 0.3645 42.02 0.75 0 1.5 0.776 +/− 0.002 0.388 39.32 0.75 0 1.5 0.780 +/− 0.002 0.390 39.12 0.75 0 1.5 0.784 +/− 0.002 0.392 38.92 0.75 0 1.5 0.796 +/− 0.002 0.398 38.34 0.75 0 1.5 0.800 +/− 0.002 0.400 38.15 0.75 0 1.5 0.804 +/− 0.002 0.402 37.97 0.75 0 1.5 0.808 +/− 0.002 0.404 37.78 0.75 0 1.5 0.812 +/− 0.002 0.406 37.61 0.75 0 1.5 0.709 +/− 0.002 0.3545 71.73 0.75 30 1.5 0.713 +/− 0.002 0.3565 70.85 0.75 30 1.5 0.717 +/− 0.002 0.3585 70.01 0.75 30 1.5 0.721 +/− 0.002 0.3605 69.21 0.75 30 1.5 0.725 +/− 0.002 0.3625 68.46 0.75 30 1.5 0.729 +/− 0.002 0.3645 67.74 0.75 30 1.5 0.776 +/− 0.002 0.388 61.07 0.75 30 1.5 0.780 +/− 0.002 0.390 60.82 0.75 30 1.5 0.784 +/− 0.002 0.392 60.17 0.75 30 1.5 0.796 +/− 0.002 0.398 58.91 0.75 30 1.5 0.800 +/− 0.002 0.400 58.51 0.75 30 1.5 0.804 +/− 0.002 0.402 58.12 0.75 30 1.5 0.808 +/− 0.002 0.404 57.74 0.75 30 1.5 0.812 +/− 0.002 0.406 57.37 0.75 30 1.5


5. A method as set forth in one of claims 1-2 characterized in that at the same time an electromagnetic wave of the wavelength λ and another electromagnetic wave of the wavelength λ/2 are passed through the crystal and the crystal is used to produce the third harmonic (⅓λ) which is of a wavelength of less than 0.450 λm.
 6. A method as set forth in claim 5 characterized in that the electromagnetic waves of the wavelengths λ and λ/2 are passed through the crystal in such a way that the propagation direction includes an angle θ+/−Δθ with the optical Z-axis and an angle φ+/−Δφ with the optical X-axis and the crystal is used to produce the third harmonic of the wavelength ⅓λ, wherein λ, θ, Δθ, φ, Δφ and ⅓ assume the values of a line in the following Table: λ ⅓ λ (μm) +/− (μm) 0.001 θ (°) Δθ (°) φ (°) Δφ (°) 0.71 0.2367 79.87 2 0 5 0.72 0.2400 75.70 2 0 5 0.73 0.2433 72.59 2 0 5 0.74 0.2467 70.03 2 0 5 0.75 0.2500 67.83 2 0 5 0.76 0.2533 65.89 2 0 5 0.77 0.2567 64.14 2 0 5 0.78 0.2600 62.55 2 0 5 0.79 0.2633 61.09 2 0 5 0.8 0.2667 59.74 2 0 5 0.81 0.2700 58.48 2 0 5 0.82 0.2733 57.30 2 0 5 0.83 0.2767 56.19 2 0 5 0.84 0.2800 55.15 2 0 5 0.85 0.2833 54.16 2 0 5 0.86 0.2867 53.23 2 0 5 0.87 0.2900 52.34 2 0 5 0.88 0.2933 51.49 2 0 5 0.89 0.2967 50.69 2 0 5 0.9 0.3000 49.92 2 0 5 0.91 0.3033 49.18 2 0 5 0.92 0.3067 48.48 2 0 5 0.93 0.3100 47.80 2 0 5 0.94 0.3133 47.15 2 0 5 0.95 0.3167 46.53 2 0 5 0.96 0.3200 45.93 2 0 5 0.97 0.3233 45.35 2 0 5 0.98 0.3267 44.79 2 0 5 0.99 0.3300 44.25 2 0 5 1 0.3333 43.74 2 0 5 1.01 0.3367 43.24 2 0 5 1.02 0.3400 42.75 2 0 5 1.03 0.3433 42.29 2 0 5 1.04 0.3467 41.84 2 0 5 1.05 0.3500 41.40 2 0 5 1.06 0.3533 40.98 2 0 5 1.07 0.3567 40.57 2 0 5 1.08 0.3600 40.17 2 0 5 1.09 0.3633 39.79 2 0 5 1.1 0.3667 39.42 2 0 5 1.11 0.3700 39.06 2 0 5 1.12 0.3733 38.71 2 0 5 1.13 0.3767 38.37 2 0 5 1.14 0.3800 38.05 2 0 5 1.15 0.3833 37.73 2 0 5 1.16 0.3867 37.42 2 0 5 1.17 0.3900 37.12 2 0 5 1.18 0.3933 36.83 2 0 5 1.19 0.3967 36.55 2 0 5 1.2 0.4000 36.27 2 0 5 1.21 0.4033 36.01 2 0 5 1.22 0.4067 35.75 2 0 5 1.23 0.4100 35.50 2 0 5 1.24 0.4133 35.26 2 0 5 1.25 0.4167 35.02 2 0 5 1.26 0.4200 34.79 2 0 5 1.27 0.4233 34.57 2 0 5 1.28 0.4267 34.35 2 0 5 1.29 0.4300 34.15 2 0 5 1.3 0.4333 33.94 2 0 5 1.31 0.4367 33.74 2 0 5 1.32 0.4400 33.55 2 0 5 1.33 0.4433 33.37 2 0 5 1.34 0.4467 33.19 2 0 5 0.88 0.2933 69.59 1.5 30 5 0.89 0.2967 67.90 1.5 30 5 0.9 0.3000 66.38 1.5 30 5 0.91 0.3033 64.98 1.5 30 5 0.92 0.3067 63.68 1.5 30 5 0.93 0.3100 62.48 1.5 30 5 0.94 0.3133 61.36 1.5 30 5 0.95 0.3167 60.30 1.5 30 5 0.96 0.3200 59.30 1.5 30 5 0.97 0.3233 58.36 1.5 30 5 0.98 0.3267 57.46 1.5 30 5 0.99 0.3300 56.61 1.5 30 5 1 0.3333 55.80 1.5 30 5 1.01 0.3367 55.03 1.5 30 5 1.02 0.3400 54.29 1.5 30 5 1.03 0.3433 53.58 1.5 30 5 1.04 0.3467 52.90 1.5 30 5 1.05 0.3500 52.25 1.5 30 5 1.06 0.3533 51.63 1.5 30 5 1.07 0.3567 51.03 1.5 30 5 1.08 0.3600 50.45 1.5 30 5 1.09 0.3633 49.89 1.5 30 5 1.1 0.3667 49.36 1.5 30 5 1.11 0.3700 48.84 1.5 30 5 1.12 0.3733 48.34 1.5 30 5 1.13 0.3767 47.86 1.5 30 5 1.14 0.3800 47.39 1.5 30 5 1.15 0.3833 46.94 1.5 30 5 1.16 0.3867 46.50 1.5 30 5 1.17 0.3900 46.08 1.5 30 5 1.18 0.3933 45.68 1.5 30 5 1.19 0.3967 45.28 1.5 30 5 1.2 0.4000 44.90 1.5 30 5 1.21 0.4033 44.53 1.5 30 5 1.22 0.4067 44.17 1.5 30 5 1.23 0.4100 43.83 1.5 30 5 1.24 0.4133 43.49 1.5 30 5 1.25 0.4167 43.16 1.5 30 5 1.26 0.4200 42.85 1.5 30 5 1.27 0.4233 42.54 1.5 30 5 1.28 0.4267 42.25 1.5 30 5 1.29 0.4300 41.96 1.5 30 5 1.3 0.4333 41.68 1.5 30 5 1.31 0.4367 41.41 1.5 30 5 1.32 0.4400 41.15 1.5 30 5 1.33 0.4433 40.89 1.5 30 5 1.34 0.4467 40.65 1.5 30 5


7. A method as set forth in one of claims 1-2 characterized in that a first electromagnetic wave of the wavelength λ₁ and a second electromagnetic wave of the wavelength λ₂ are passed through the crystal in such a way that the propagation direction includes an angle θ+/−Δθ with the optical Z-axis and an angle φ+/−Δφ with the optical X-axis and the crystal is used to produce an electromagnetic wave of the wavelength λ₃=λ₁·λ₂/(λ₁+λ₂) which is of a wavelength of less than 0.450 μm.
 8. A method as set forth in one of claims 1-2 characterized in that a f_(i)rst electromagnetic wave of the wavelength λ₃ and a second electromagnetic wave of the wavelength λ₂ are passed through the crystal in such a way that the propagation direction includes an angle θ+/−Δθ with the optical Z-axis and an angle φ+/−Δφ with the optical X-axis and the crystal is used to produce an electromagnetic wave of the wavelength λ₁=λ₂·λ₃/(λ₂−λ₃) which is of a wavelength of less than 0.450 μm.
 9. A method as set forth in one of claims 1-2 characterized in that an electromagnetic wave of the frequency λ₃ is passed through the crystal in such a way that the propagation direction includes an angle θ+/−Δθ with the optical Z-axis and an angle φ+/−Δφ with the optical X-axis and the crystal is used to produce an electromagnetic wave of the wavelength λ₁ and an electromagnetic wave of the wavelength λ₂ so that λ₃=λ₁·λ₂/(λ₁+λ₂).
 10. A method as set forth in one of claims 7 characterized in that λ₁, λ₂, λ₃, θ, Δθ, φ, Δφ assume the values of a line of the following Table: λ₁ λ₂ λ₃ Type I (μm) +/− (μm) +/− (μm) +/− Theta (°) +/− Δθ 0.015 0.015 0.010 3.0° (°) φ (°) Δφ (°) 0.810 0.632 0.355 42.9 3.0 0 5 1.064 0.532 0.355 40.8 3.0 0 5 0.642 0.454 0.266 64.5 3.0 0 5 0.722 0.421 0.266 62.2 3.0 0 5 0.812 0.396 0.266 59.6 3.0 0 5 0.982 0.365 0.266 55.1 3.0 0 5 1.062 0.355 0.266 53.3 3.0 0 5 1.342 0.332 0.266 48.0 3.0 0 5 1.064 0.266 0.213 72.1 3.0 0 5 1.326 0.254 0.213 61.5 3.0 0 5 0.720 0.355 0.238 77.8 3.0 0 5 0.720 0.520 0.302 52.4 3.0 0 5 0.910 0.720 0.402 37.7 3.0 0 5 0.910 0.808 0.428 35.8 3.0 0 5 1.064 0.532 0.355 40.8 3.0 0 5 1.062 0.589 0.379 38.7 3.0 0 5 1.062 0.751 0.440 34.6 3.0 0 5 0.810 0.632 0.355 62.6 2.5 30 5 1.064 0.532 0.355 51.5 2.5 30 5 0.982 0.365 0.266 70.0 2.5 30 5 1.062 0.355 0.266 64.9 2.5 30 5 1.342 0.332 0.266 54.4 2.5 30 5 1.326 0.254 0.213 69.9 2.5 30 5 0.910 0.720 0.402 53.0 2.5 30 5 0.910 0.808 0.428 51.5 2.5 30 5 1.064 0.532 0.355 51.4 2.5 30 5 1.062 0.589 0.379 49.5 2.5 30 5 1.062 0.751 0.440 46.2 2.5 30 5 0.910 0.720 0.402 64.2 2.5 30 5 0.910 0.808 0.428 56.3 2.5 30 5 1.062 0.751 0.440 59.5 2.5 30 5


11. A method as set forth in claim 10 characterized in that Δφ=1.5°.
 12. Use of a crystal of the family A_(x)M_(1-x)X₃(BO₃)₄ as a non-linear optical element to produce light of a wavelength of less than 0.450 μm, wherein both A and also M stand for an element from the group Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, A≠M and X═Al, Ga, Sc and 0≦x≦1.
 13. A crystal of the family A_(x)M_(1-x)X₃(BO₃)₄, wherein both A and also M stand for an element from the group Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, A≠M and X═Al, Ga, Sc and 0≦x≦1, wherein the crystal has at least two substantially flat end faces, characterized in that at least one end face is oriented with respect to the crystallographic axes in such a way that upon normal incidence of an electromagnetic wave or two electromagnetic waves of differing wavelength onto said end face due to a non-linear optical effect an electromagnetic wave of a wavelength of less than 0.450 μm is produced.
 14. A crystal of the family A_(x)M_(1-x)X₃(BO₃)₄, wherein both A and also M stand for an element from the group Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu, A≠M and X═Al, Ga, Sc and 0≦x≦1, wherein the crystal has at least two substantially flat end faces, characterized in that at least one end face is oriented with respect to the crystallographic axes in such a way that upon incidence of an electromagnetic wave or two electromagnetic waves of differing wavelength onto said end face at the Brewster angle due to a non-linear optical effect an electromagnetic wave of a wavelength of less than 0.450 μm is produced. 